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A007984
Number of essential graphs with n nodes (in 1-1 correspondence with Markov equivalence classes of acyclic digraphs).
5
1, 2, 11, 185, 8782, 1067825, 312510571, 212133402500, 326266056291213, 1118902054495975181, 8455790399687227104576, 139537050182278289405732939, 4991058955493997577840793161279
OFFSET
1,2
REFERENCES
S. B. Gillispie and M. D. Perlman, Enumerating Markov equivalence classes of acyclic digraph models, Proc. of Conf. on Uncertainty in Artificial Intelligence (2001), 171-177.
S. B. Gillispie and M. D. Perlman, The size distribution for Markov equivalence classes of acyclic digraph models, Artificial Intelligence, 141 (2002), 137-155.
Bertran Steinsky, Enumeration of Labelled Essential Graphs, Ars Comb., 111, (2013), 485-494
LINKS
S. B. Gillispie and M. D. Perlman, Enumerating Markov equivalence classes of acyclic digraph models, Univ. of Washington, Dept. of Statistics, Technical Reports.
S. B. Gillispie and M. D. Perlman, The size distribution for Markov equivalence classes of acyclic digraph models, Univ. of Washington, Dept. of Statistics, Technical Reports.
Zehao Jin, Mario Pasquato, Benjamin L. Davis, Tristan Deleu, Yu Luo, Changhyun Cho, Pablo Lemos, Laurence Perreault-Levasseur, Yoshua Bengio, Xi Kang, Andrea Valerio Maccio, and Yashar Hezaveh, A Data-driven Discovery of the Causal Connection between Galaxy and Black Hole Evolution, arXiv:2410.00965 [astro-ph.GA], 2024. See p. 33.
CROSSREFS
Cf. A368569 (refined by # arcs).
Sequence in context: A124836 A365361 A013104 * A132871 A140314 A226052
KEYWORD
nonn,changed
AUTHOR
David Madigan (madigan(AT)stat.washington.edu)
EXTENSIONS
More terms from Steven B. Gillispie (gillisp(AT)u.washington.edu), Oct 21 2003
a(10) corrected by Steven B. Gillispie (gillisp(AT)u.washington.edu), Aug 14 2007, who says: I have learned from Bertran Steinsky (who determined the correct number) that there was an error in my computer software that computed a(10). The correct value is 1118902054495975181.
a(11)-a(13) from Bertran Steinsky, Jun 24 2013
STATUS
approved